I have been amazed at how easy it is to tell an Airbus apart from a Boeing just by looking at its wing. The Boeing wing consists of several flaps with fewer ailerons...the Airbus wing appears to have a lot more ailerons. What are the advantages that each wing gets from these very different arrangements of ailerons? Also, why does Boeing try to avoid wingtip fences, yet Airbus tries to avoid blended winglets and raked wingtips?

Boeing wings tend to have inboard high speed ailerons and outboard low speed ailerons. The exceptions are the 737 and 757, which only have outboard ailerons. All Boeings have leading edge devices, usually a mixture of Krueger flaps (707, inboard on 727 and 737, variable camber on 747 and I'm told on the 787) and slats (outboard on 727, 737, full span on 757, 767 and 777). Boeing rarely uses winglets (747-400 787-3 are the exceptions and the 737-700 and 737-800 are available with APB winglets). Instead, they are getting hooked on raked wingtips (767-400, 777-300ER, 787-8 and 787-9). All Boeing have spoilers that are used for roll control at higher speeds and as lift dumpers. Boeing originated the idea of using spoiler for roll control on the B-47, to counter aileron reversal from wing torsional windup.

Airbus used inboard high speed ailerons and outboard low speed ailerons on the A300B2 & B4. In an unusual move, on the A310 they got rid of the low speed ailerons, and this carried over onto the A300-600. The A318/319/320/321, A330/340 and A380 only have outboard ailerons. Airbus uses full-span slats on all their aircraft, but I know that some A300s (and possibly the A310) have a single Krueger flap segment inboard at the wing root. Airbus uses spoilers the same way as Boeing. Airbus has added small winglets to the A310, A300-600, A318/319/320/321 (except the A320-100) and the A380. On the A330/340 the winglet is bigger, but still not as big as the APB winglets.

For completeness sake, Douglas has full-span slats on the DC-9 and DC-10. On the DC-8, they have slots that opened up inboard of the pylons. The DC-10 has inboard high speed ailerons and outboard low speed ailerons. The DC-8 (I think) and the DC-9 only have outboard ailerons. Douglas never used winglets (except on the MD-11) and also used spoilers like Boeing and Airbus.

Differently design philosophy, I guess. Airbus makes their flaps extending all the way across the wing, even though they're not actually a single unit. Boeing goes for deeper flaps with more travel, but they're segmented (they have to be to avoid engine exhaust).

The DC-10/MD-11 are roughly the same as Boeing's widebodies (flap-wise)

All Boeing and Airbus flaps are Fowler flaps, which translate aft and then pivot down. Douglas used Single Pivot flaps, which moved similar to Fowler flaps.

The high speed ailerons I referred to are the gap you see in the DC-10, A300, A310, 707, 727, 747, 767 and 777 flaps. The idea was to provide a path for the engine exhaust.

One other detail - airliner wings typical have "Yehudis", where the trailing edge is extended in the inboard area. This provides depth to contain the landing gear stub spar. Its easier to make the flap in this area a separate piece, as opposed to part of a bigger piece.